OK. Before now, I had jailbroken my iOS (6.1.2) and was going fine until without giving any thoughts, I hit the update button in the iTunes (6.1.4). And since then, my iphone 5 is stuck on the itunes logo and the connector. The iTunes has stopped recognising my device and giving error of connection timed out. I NEED HELP HERE !!

UPDATE:
I have tried putting the phone into DFU mode through recovery mode but no use. I do hear connect/disconnect sounds and the screen goes completely black (DFU mode) but itunes still doesn't recognise my device.

Try just recovery mode...turn phone off, hold home button down while plugging in sync cable..see if iTunes sees phone in recovery mode-restore...

Yeah...should never update a JB phone..

If Recovery mode doesn't work, then try DFU again..or maybe a different cable...make sure u select the restore option and not update... Make sure the phone port is clear of lint etc..If DFU still isn't working I'd reboot PC...if that still doesn't help I'd uninstall iTunes and reinstall..